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(2x-1)(3x+1)+(3x+4)(3-2x)=5

2 min read Jun 16, 2024
(2x-1)(3x+1)+(3x+4)(3-2x)=5

Solving the Equation: (2x-1)(3x+1)+(3x+4)(3-2x)=5

This article will guide you through the steps to solve the given equation: (2x-1)(3x+1)+(3x+4)(3-2x)=5.

Step 1: Expand the Products

First, we need to expand the products on the left side of the equation. We can use the FOIL method (First, Outer, Inner, Last) for this.

  • (2x-1)(3x+1):

    • First: (2x)(3x) = 6x²
    • Outer: (2x)(1) = 2x
    • Inner: (-1)(3x) = -3x
    • Last: (-1)(1) = -1

  • (3x+4)(3-2x):

    • First: (3x)(3) = 9x
    • Outer: (3x)(-2x) = -6x²
    • Inner: (4)(3) = 12
    • Last: (4)(-2x) = -8x

Now, rewrite the equation: 6x² + 2x - 3x - 1 + 9x - 6x² + 12 - 8x = 5

Step 2: Combine Like Terms

Simplify the equation by combining terms with the same variable and exponents.

  • x² terms: 6x² - 6x² = 0
  • x terms: 2x - 3x + 9x - 8x = 0
  • Constant terms: -1 + 12 = 11

Now the equation looks like this: 0 + 0 + 11 = 5

Step 3: Solve for x

We are left with 11 = 5, which is clearly a false statement. This indicates that there is no solution to the equation.

Therefore, the equation (2x-1)(3x+1)+(3x+4)(3-2x)=5 has no solution.

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